Simulation code of transient flow in shallow water
SARA COELHO DA SILVA1; Eloy Kaviski2; Liliana Madalena Gramani2; Adilandri Mércio Lobeiro1
1 Universidade Tecnológica Federal do Paraná UTFPR; 2 Universidade Federal do Paraná UFPR
doi:10.20906/CPS/CILAMCE2017-0022
Resumo
The mathematical model that represent hydrodynamics in a body of water are based on the equation of continuity and momentum. The model presentes in this article was formulated to simulate flow in shallow water, where the lenght of water body is much greater than the depth, neglecting the vertical chances and tensions. On this way, the shallow water equation were used and a computational simulation of the transient two dimensional hydrodynamics flow was programmer in a reservoir, in order to determine the water surface level and velocity componentes at each instante of time, to each point of the two dimensional domain. For linearization of the shallow water equation, a rectangular mesh and the finite volume method were used. In the temporal discretization, an implicit scheme was used, whose computational efficiency proved superior to the explicit scheme, with unconditional stability. Because it is a strongly advected model, the upwind scheme proved to be the most adequate in spatial processing. The solution of the system of linearized equations of the model, was obtained by the iterative method of Gauss Seidel, using a code implemented in FORTRAN Language. In order to validate the model, a flow simulation was performed in a reservoir, based on data such as the initial level and flow rate at the outlets. The algorithm developed allowed the temporal evaluation of the level and the flow in the reservoir, allowing change in the contour conditional at any instante of time. The post processing of the code was used in the graphical analysis of the model, demonstrating fidelity with the physical phenomenon investigated. In the numerical validation of the model, the stability and precision of the model were tested. In the estimation of the error we used mesh refinement and the Richardson estimator, obtaining residues very close to zero with a small number of iterations, indicating very low computational cost. The algorithm developed for shallow water flow simulation showed good accuracy, stability and high computational ef
Palavras-chave: Computer code; FORTRAN; implicit scheme; finite volume; shallow water